Algorithmically designed lace tessellations

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Plain woven cloth (C T C) and tri-axial weave (C T) appear frequently in bobbin lace motifs. The key to these weaving patterns is that they can be made in a two-by-two grid. In plain weave, two worker threads weave through two passive threads giving the four threads at a time that bobbin lacemakers usually work with. This week on the Arachne news group, Joseph Young asked whether lacemakers have tried any other weaving patterns: https://www.mail-archive.com/lace@arachne.com/msg53321.html

This question intrigued me so I decided to give 2/2 twill a try using the usual bobbin lace techniques.

The twill pattern requires a four-by-four grid to get a full repeat so I tried weaving two worker threads though four passive threads, that is working with 6 threads (three pairs) at a time.

Within these six threads, you can treat two threads as if they are one (as is sometimes done in lazy crossings) so that you can still use a modified cross and twist action. Here is how I broke down the steps for one repeat:

Steps

Weaving from left to right:

When weaving from right to left you need to change the actions just a little bit to complete the second half of the pattern:

Notes:

If you do not have a multiple of 4 passives, you will have 2 extra passives on each row. Do a regular cloth stitch (C T C) through these two threads at the beginning of the left to right row and at the end of the right to left row.

If you do not add a footside or connect the twill to some other ground or cloth area, you will need to twist the workers a few times at the end of each row (not shown in diagram) or the worker threads will slide past the passive threads at the left edge.

Reversing the twill direction

You can also change the direction of the twill. Instead of the horizontal bars heading south-east, you can make the bars head south-west.

This can be easily done by modifying the first two steps from before:

Other variations

You can also combine south-east and south-west patterns to create more complicated designs such as diamond twill. Using one colour for the passives and another colour for the workers should make the twill pattern stand out.

Examples

I have worked a few variations on a 2mm x 2mm grid using 60 DMC Cordonet Special thread. Left to right: Several rows of SW, several rows of SE, diamonds, zigzags, adding twists on the passives, plain weave. The plain weave serves as a comparison for density. I added a twist to pairs of passive that were both sitting on top of the worker thread which resulted in ‘x’s in the colour of the passive thread

I was able to work the twill sections almost as quickly as the plain cloth section, once I got into the rhythm.

Several twill patterns worked with bobbins.

As Gabriele mentioned on Arachne (https://www.mail-archive.com/lace@arachne.com/msg53323.html), the threads in twill can slide around, much more than for plain weave. When the piece was finished, I pushed on the cloth with my thumb to see how stable it was. It took a lot of pushing to disturb the plain weave but the twill distorted with very little effort. The first two sections, worked in all SW or all SE, were the most stable, the diamonds were the most unstable. I think the more passive threads that the workers skip over, the weaker the material will be. If I were to use this technique in a lace piece, I would make the rows closer together (probably 2mm x 1.5mm for the sample above) and I would use a thread that is not slippery.